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EMF and Terminal Voltage
Recall: An electric circuit needs a potential difference to
make current flow. Sources of potential difference can
be called different things:
• power supply
• source of emf (E ) – electromotive force
Ex: battery or generator are power supplies or have emf
A battery is a nearly constant voltage source, but it does
have a small internal resistance (r), which reduces the
actual, aka terminal voltage, Vab, from the ideal emf,E.
This resistance behaves as if wired in series with the emf
Electrical Circuits
Circuit – a complete path from the high to low potential
which includes a load between the two potentials
 If there’s no load - only direct connection from high
to low - then it’s called a short (circuit) – dangerous…
 If there’s a switch: open = no flow; closed = flow
 There are only “one way streets” in any circuit –
Current cannot/will not flow in 2 directions within a
wire as it is always forced to the lower potential
and that’s only going to be in one direction along any
particular path – called a branch – of a circuit.
 Recall: Current/individual charges do not bunch up or
concentrate in certain places in a circuit:
there’s always a continuous flow,
& they’re not used up – conservation of charge!
(03) Examples of Basic Series Circuits
Schematic Diagrams
Diagrams that depict electrical
circuits using special symbols
to represent each component
of the circuit.
Why? Standardized and
easier to draw/interpret.
Know these:
Series Circuits
Series: have only one pathway from the high to
the low potential, so
► I is same everywhere.
Itotal = I1 = I2 = I3 = …
► R’s add together.
Req = R1 + R2 + R3 + …
► V’s add together.
Vtotal = V1 + V2 + V3 + …



where Vtotal is the voltage “boost” of the battery
and V1, V2 etc are the voltage “drops” of the loads
following Conservation of NRG: ΔVloop = 0
called Kirchhoff’s Loop Rule… coming up
Schematic Diagrams – Series Circuit
I is the same everywhere
R’s add to find total Req
V drops around loop add to = V boost of battery
Series Circuits
Applying Ohm’s Law
Itotal = Vtotal /Req = Ianywhere
and
Ianywhere = V1 / R1 = V2 / R2 = V3 / R3 =…
Advantage?
Cheap – use much less wiring than parallel
Disadvantage?
If anything breaks, opens, etc, nothing works!
Ex: old strands of Christmas lights
Parallel Circuits
Parallel have multiple branches from
the high to the low potential, so
► I divides up among the branches
Itotal = Ib1 + Ib2 + Ib3 +…
 Amt in each branch depends inversely
on the R that’s there
► V’s are the same across each branch.
Vtotal = Vb1 = Vb2 = Vb3 = …
► Req decreases as more resistors are added,
 Since we might be adding another R (stop light)
but we’ve also added a brand new path (road)…
1/Req = 1/Rb1 + 1/Rb2 + 1/Rb3 + …
Schematic Diagrams – Parallel Circuit
In parallel, I is split
V in every branch = V of battery
R’s add by inverse equation
Parallel Circuits
Applying Ohm’s Law
Vtotal = ItotalReq = Vanybranch
and
Vanybranch = Ib1Rb1 = Ib2Rb2 = Ib3Rb3 = …
Advantage?
Maintains a constant V drop across each parallel
branch, so any number of loads can be plugged in
and all will get current as if they’re alone – nothing
affects anything else!
Disadvantage?
Must be connected to circuit breaker as more loads
reduce Rtotal so Itotal will increase – dangerous!
Ex: just about everything - everywhere!!!
Kirchhoff’s Rules
Some circuits cannot be
broken down into series
and parallel connections.
For these circuits we use
Kirchhoff’s rules.
Named after Gustav
Kirchhoff when he
pushlished them in 1845.
Kirchhoff’s Rules
Junction Rule: The sum of currents entering a junction
equals the sum of the currents leaving it.
Origin?
The Law of Conservation of Charge
Kirchhoff’s Rules
Loop Rule: The sum of the changes in potential around
a closed loop is zero.
Origin?
The Law of Conservation of Energy
Problem Solving: Kirchhoff’s Rules
1. Label each current, using I’s with subscripts.
2. Identify unknowns.
3. Apply junction and loop rules; you will need as many
independent equations as there are unknowns.
4. Solve the equations, being careful with signs.
Meters to Take Circuit Measurements
► Ammeters
measure current. They must be connected
right into the path of the current to get a read of how
much I is traveling through the circuit at that point. So
they must be connected in __________ with the branch
of the circuit they’re to measure.
The construct of an ammeter has as _____ resistance as
possible, so that it doesn’t alter the circuit you’re
putting it in to measure.
► Voltmeters
measure voltage, or potential difference.
They must be connected across the part of the circuit
for which you want a read of voltage drop. So they
must be connected in __________ with the branch of
the circuit they’re to measure.
The construct of a voltmeter has as ____ a resistance as
possible, so that it, again, doesn’t alter the circuit
you’re putting it in to measure… no I will go that way.
Meters to Take Circuit Measurements
►
Ohmmeters measure resistance and they’re construct is
simply a combo of both that of a ammeter and voltmeter.
►
Multimeters are the most useful – they have a dial or
switch that can be set to measure any of these quantities
Analog vs Digital Meters
 Analog – reading from a needle pointer on a scale
► uses a galvanometer – works on the principle of
force between a magnetic field and a currentcarrying wire… more on that in Ch 20
 Digital – reading from a LCD
►No galvanometer – instead “newer” electronic
circuitry…
►Much more precision… but not necessarily accurate…